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The Crossover Design Cookbook
Chapter 2: How Components Work
by Mark Lawrence

## Inductors

Inductors are coils of wire; in fact, during the days of vacuum tubes they were called coils. The unit of inductance is the Henry. One henry is a very large inductor.

An inductor works like the mass of the water in a hose. If you had a two hundred foot long 4 inch diameter fire hose going full blast, and instantly cut off the water supply, the hose will not instantly stop spraying water. Inside this hose there are about 125 gallons of water weighing over 1,000 lbs. The momentum of the moving water in the hose will keep the water flowing for some time. You can't instantly stop 1,000 lbs. Similarly, an inductor adds "mass" to electric current: an inductor makes it harder to build up a current flow in a wire, and then once the current is flowing, the inductor makes it harder to stop the current.

If you connect two inductors end to end in a line, the inductances add. If you connect them side by side, the formula for the new inductance is the same as the parallel resistance law. So, inductors combine like resistors. People almost never combine inductors in either of these ways.

There are two ways to build inductors: air core and iron or ferrite core. Iron core inductors are cheaper, lighter, smaller, and are available in larger values. As usual, there's no free lunch. The inductor works by storing energy inside the coils in a magnetic field. The substance inside the coils effects how the energy is stored. Iron stores magnetic energy much more efficiently than air. However, at some point the iron core saturates: it is holding all the magnetic field it possibly can and stops storing more energy. At this point, the iron core inductor starts acting like an air core inductor, and the inductance value suddenly drops by a factor of 2 to 100. Iron or Ferrite core inductors come with the iron shaped in lots of different ways. Pretty much the only thing that matters is the amount of iron, not whether it's a bobbin or a bar or a donut or whatever.
L = L1 + L2
 L1 * L2 L = L1 + L2
SeriesParallel

Core saturation produces non-linearities which sound completely awful. Because of this, many speaker builders will only use air core inductors. However, iron core inductors are just fine as long as you don't get them near saturation. Iron core inductors are often rated for maximum watts. If you use iron core inductors, get 300 watt devices minimum, preferably 500 watt devices. It's difficult to predict core saturation. You basically have to get a sample inductor, and then start running current through it, measuring the impedance. At some particular current as you add more the impedance will suddenly drop. This is the point of core saturation, and the maximum useful current for this inductor.

Air core inductors also experience something like core saturation, but only at energy levels which would interest physicists. Even a Krell KSA 1,000 isn't going to get close.

The basic law for inductors is:

Z = 2πf L

where "Z" is the effective resistance, or impedance, of inductor "L" at frequency "f". As you can see from this law, at very low frequencies an inductor has very little resistance and acts like a short circuit, or a short piece of wire. At very high frequencies an inductor has large resistance, and acts like an open circuit, which is almost like having no connection at all. In between low and high frequencies, the inductor has intermediate resistance, which is the effect we use to produce crossovers.

If you connect two inductors in series to a voltage, the voltage is divided between the two inductors exactly as it would be divided by two resistors. Even though the effective resistance of each inductor is raising with frequency, the two inductors are raising at the same rate, so this effect cancels. Again, we're never going to connect inductors like this. Inductors are very expensive, and the last thing we're going to want to do is to buy two very expensive components and combine them to make one cheap component.

### An inductor connected in series with a resistor

 1 V1 = V * 1 + 2π L f / R